wow, thank you very much for explaining that to me... I spent at least an hour reading my book and a few websites and I didn't get it until just now (maybe I'm too tired)

would the solution process differ greatly if we were trying to find the Taylor series and not the Maclaurin series (not at a = 0)?

The process wouldn't differ, i.e. if you wanted to take the Taylor Series of a polynomial about x = a you would evaluate all your derivatives at x = a instead of at x = 0. As an example, if I took the Taylor series of the general 3rd degree polynomial at x = 1 I'd have